wp.t {WebPower}

Statistical Power Analysis for t-Tests

Description

A t-test is a statistical hypothesis test in which the test statistic follows a Student's t distribution if the null hypothesis is true and follows a non-central t distribution if the alternative hypothesis is true. The t test can assess the statistical significance of (1) the difference between population mean and a specific value, (2) the difference between two independent populaion means, and (3) difference between means of matched paires.

Usage

wp.t(n1 = NULL, n2 = NULL, d = NULL, alpha = 0.05, power = NULL,
  type = c("two.sample", "one.sample", "paired", "two.sample.2n"),
  alternative = c("two.sided", "less", "greater"),
  tol = .Machine$double.eps^0.25)

Arguments

n1

Sample size of the first group.

n2

Sample size of the second group if applicable.

d

Effect size. See the book by Cohen (1988) for details.

alpha

Significance level chosed for the test. It equals 0.05 by default.

power

Statistical power.

type

Type of comparison ("one.sample" or "two.sample" or "two.sample.2n" or "two.sample.2n" or "paired"). "two.sample" is two-sample t-test with equal sample sizes, two.sample.2n" is two-sample t-test with unequal sample sizes, "paired" is paired t-test

alternative

Direction of the alternative hypothesis ("two.sided" or "less" or "greater"). The default is "two.sided".

tol

tolerance in root solver.

Value

An object of the power analysis.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed). Hillsdale, NJ: Lawrence Erlbaum Associates.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

Examples

#To calculate the power for one sample t-test given sample size and effect size:
wp.t(n1=150, d=0.2, type="one.sample")
#  One-sample t-test
#
#	n   d alpha    power
#	150	0.2	0.05	0.682153
#
#  URL: http://psychstat.org/ttest

#To calculate the power for paired t-test given sample size and effect size:
wp.t(n1=40, d=-0.4, type="paired", alternative="less")
#  Paired t-test
#
#     n    d alpha     power
#    40 -0.4  0.05 0.7997378
#
#  NOTE: n is number of *pairs*
#  URL: http://psychstat.org/ttest

#To estimate the required sample size given power and effect size for paired t-test :
wp.t(d=0.4, power=0.8, type="paired", alternative="greater")
#  Paired t-test
#
#           n   d alpha power
#    40.02908 0.4  0.05   0.8
#
#  NOTE: n is number of *pairs*
#  URL: http://psychstat.org/ttest

#To estimate the power for balanced two-sample t-test given sample size and effect size:
wp.t(n1=70, d=0.3, type="two.sample", alternative="greater")
#  Two-sample t-test
#
#     n   d alpha     power
#    70 0.3  0.05 0.5482577
#
#  NOTE: n is number in *each* group
#  URL: http://psychstat.org/ttest

#To estimate the power for unbalanced two-sample t-test given sample size and effect size:
wp.t(n1=30, n2=40, d=0.356, type="two.sample.2n", alternative="two.sided")
#  Unbalanced two-sample t-test
#
#    n1 n2     d alpha     power
#    30 40 0.356  0.05 0.3064767
#
#  NOTE: n1 and n2 are number in *each* group
#  URL: http://psychstat.org/ttest2n

#To estimate the power curve for unbalanced two-sample t-test given a sequence of effect sizes:
res <- wp.t(n1=30, n2=40, d=seq(0.2,0.8,0.05), type="two.sample.2n",
                                             alternative="two.sided")
res
#  Unbalanced two-sample t-test
#
#    n1 n2    d alpha     power
#    30 40 0.20  0.05 0.1291567
#    30 40 0.25  0.05 0.1751916
#    30 40 0.30  0.05 0.2317880
#    30 40 0.35  0.05 0.2979681
#    30 40 0.40  0.05 0.3719259
#    30 40 0.45  0.05 0.4510800
#    30 40 0.50  0.05 0.5322896
#    30 40 0.55  0.05 0.6121937
#    30 40 0.60  0.05 0.6876059
#    30 40 0.65  0.05 0.7558815
#    30 40 0.70  0.05 0.8151817
#    30 40 0.75  0.05 0.8645929
#    30 40 0.80  0.05 0.9040910
#
#  NOTE: n1 and n2 are number in *each* group
#  URL: http://psychstat.org/ttest2n

#To plot a power curve:
plot(res, xvar='d', yvar='power')